Yes the big fish get attention and the small fish get ignored. Welcome to the B2B universe. If you're a small business relative to the scope of your counterparty, you generally won't get good service or have any leverage.
Seek out resellers or providers who are closer to yourself in size. You want it to hurt a bit if they lose your business. Of course you can go too far the other way as well, if you're a large client of a small company you'll probably get good service but they will be living parasitically off of you which isn't healthy and they may not be able to respond quickly enough if your needs grow.
I see this for actual service providers that have full control over their business, but if you have resellers of similar size as your own org, don't you end up with the problem that they are about as important for the big provider as you are and you are as screwed as before when things go wrong?
Seek out resellers or providers who are closer to yourself in size. You want it to hurt a bit if they lose your business. Of course you can go too far the other way as well, if you're a large client of a small company you'll probably get good service but they will be living parasitically off of you which isn't healthy and they may not be able to respond quickly enough if your needs grow.